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Unformatted text preview: AMS507 Introduction to Probability  Midterm II Fall 2009 Your name: Your ID number: You shall receive 10 points for each of the following 10 question. The total will be divided by 10. The maximum score is 10. 1. The random variable X has probability density function f ( x ) = (  x  if  x  ≤ 1 otherwise . Find E [ X ] and V ar ( X ). 2. Suppose that X is uniformly distributed in [ 2 , 2]. Find the proba bility density function of the random variable Y = X 6 . 1 3. Let X and Y be independent geometric random variables with pa rameters 0 . 5 and 0 . 25, respectively. Find P ( X = Y ). 4. The annual rainfall (in inches) in a certain region is normally dis tributed with μ = 40 and σ = 4. What is the probability that, starting with this year, it will take over 10 years before a year occurs having a rainfall of over 50 inches? What assumptions are you making? 2 5. I am selling my house, and have decided to accept the first offer exceeding $ K . Assuming that offers are independent exponential random....
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 Spring '08
 Feinberg,E
 Probability theory, probability density function, 10 Years, 50 inches

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